Method of determination of gas properties at reference conditions

ABSTRACT

A method of determination of gas properties at reference conditions of temperature and pressure. This determination is needed in systems including mass flow meters, combustion control systems, gas meters and the like. The system disclosed enables the determination of properties including specific heat and thermal conductivity at reference conditions.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method for the determination ofcertain physical properties of fluids and more particularly thedetermination of these properties at given reference conditions oftemperature and pressure.

2. Background

Traditionally the determination of these properties of fluids at givenreference conditions of temperature and pressure has been achieved bytemperature and/or pressure control of the gas or liquid of interest, orby means of composition analysis without such controls, either of theseat great cost in hardware and energy. This also makes battery poweredoperation unattractive.

In the copending application Ser. No. 210,892, filed Jun. 24, 1988,entitled "Measurement of Thermal Conductivity and Specific Heat", nowU.S. Pat. No. 4,944,035, assigned to the same assignee as the presentinvention and incorporated herein by reference to the extent needed,there is described that in the prior art determination of specific heat,c_(p), has been via calorimetry using reversible step increases ofenergy fed to a thermally isolated or adiabatic system. Such devices arebulky, slow and cumbersome.

With respect to measuring thermal conductivity in fluids various typesof detectors have been used. This includes resistance bridge typesensors. One such device is described in U.S. Pat. No. 4,735,082 inwhich thermal conductivity is detected using a Wheatstone bridgetechnique in which a filament in one diagonal of the bridge is placed orpositioned in a cavity through which the sample gas of interest ispassed. The filament is used to introduce a series of amounts of thermalenergy into the fluid of interest at alternating levels by varying theinput voltage which, are, in turn, detected at the other diagonal asvoltage difference signals. Integration of the changes of the value ofthe successive stream of signals yields a signal indicative of the heatdissipation through the fluid, and thus, the thermal conductivity of thefluid.

Further to the measurement of thermally induced changes in electricalresistance, as will be discussed in greater detail below, especiallywith reference to prior art FIGS. 1-5, recently very small and veryaccurate "microbridge" semiconductor chip sensors have been described inwhich etched semiconductor "microbridges" are used as condition or flowsensors. Such sensors might include, for example, a pair of thin filmsensors around a thin film heater. Semiconductor chip sensors of theclass described are treated in a more detailed manner in one or more ofpatents such as U.S. Pat. Nos. 4,478,076, 4,478,077, 4,501,144,4,651,564 and 4,683,159, all of common assignee with the presentinvention.

It is apparent, however, that it has been necessary in the past toaddress the measurement of specific heat c_(p), and thermal conductance,k, of a fluid of interest with separate and distinct devices. Not onlyis this quite expensive, it also has other drawbacks. For example, thenecessity of separate instruments to determine specific heat and thermalconductivity may not allow the data consistency and accuracy needed foruseful fluid process stream (gas or liquid) characterization because therequired degree of correlation may not be present.

The copending application referred to above addresses an invention whichovercomes many disadvantages associated with the determination of bothspecific heat, c_(p), and thermal conductivity, k, by providing simpletechniques which allow accurate determination of both properties in asample of interest using a single sensing system. That inventioncontemplates generating an energy or temperature pulse in one or moreheater elements disposed in and closely coupled to the fluid medium (gasor liquid) of interest. Characteristic values of k and c_(p) of thefluid of interest then cause corresponding changes in the time variabletemperature response of the heater to the pulse. Under relatively staticsample flow conditions this, in turn, induces corresponding changes inthe time-variable response of one or more temperature responsive sensorcoupled to the heater principally via the fluid medium of interest.

The thermal pulse of a source need be only of sufficient duration thatthe heater achieves a substantially steady-state temperature for a shorttime. This pulse produces both steady-state and transient conditions atthe sensor. Thermal conductivity, k, and specific heat, c_(p), can besensed within the same sensed thermal pulse by using the steady-statetemperature plateau to determine k which is then used with the rate ofchange of temperature in the transient condition to determine c_(p).

SUMMARY OF THE INVENTION

The present invention describes a method of determination of fluidproperties at reference conditions of temperature and pressure. Thisdetermination is needed in various systems including mass flow meters,combustion control systems, gas meters, heating value or energy flowmeters and gas density sensors. In this invention the method is based onusing the fluid properties as measured, i.e., under non-referenceconditions of pressure or temperature, without analyzing for compositionor sensing pressure, and exercising any of a number of derivedcomputational options to arrive at the property values of interest underthe chosen reference conditions of pressure and temperature. Of specialinterest are the properties of thermal conductivity and specific heat ofgases, and specifically of fuel gases and material gases.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1, 2, and 3 are different views of a prior art embodiment of amicrobridge flow sensor.

FIGS. 4 and 5 are typical circuits for use with the sensors of FIGS.1-3.

FIG. 6 is a schematic representation of sensor time/temperature responsecurves according to a heater pulse.

FIGS. 7a, 7b, and 7c, represent several heater/sensor configurations ofmicrobridge systems in accordance with the invention.

FIG. 8 is a scanning-electron-microscope (SEM) photo of themicrostructure of a typical microbridge sensor.

FIG. 9 is a partial schematic and block diagram of a circuit for usewith a sensor as depicted in FIG. 7(b) in accordance with the invention.

FIG. 9a is a more detailed circuit schematic with reference to FIG. 7c.

FIG. 10 is a schematic block diagram of the system of the inventionincluding calibration and use functions.

FIG. 11 is a scope trace representing the temperature signal rise versustime, for the configuration of FIG. 7(c) in response to a heater pulsefor dry air at atmospheric pressure,

FIG. 12 is a graphical representation of the temperature signal riseversus time, for the configuration of FIG. 7(c) in response to theheater pulse for various gases at atmospheric pressure as indicated.

FIG. 13 is a graphical representation of thermal conductivitydetermination based on the bridge output of FIG. 9(a).

FIG. 14 is a theoretical graphical representation of sensor heat-up timeversus pressure for several gases using the sensor configuration of FIG.7b.

FIG. 15 is similar to FIG. 14 based on data taken by a sensor of thetype depicted in FIG. 7(b) calculated in accordance with the invention.

FIG. 16 is a graphical representation of sensor heat-up time versuspressure for several gases using the sensor configuration of FIG. 7c.

FIG. 17 is a graphical representation of sensor cooling time versuspressure for several gases using the sensor configuration of FIG. 7c.

FIG. 18 shows graphically the relation between the specific heat ofseveral gases versus thermal conductivity.

FIGS. 19 and 20 show thermal conductivity versus temperature from HBK,Chem. & Phys. 67th ed. for several gases.

FIG. 21 shows specific heats of several gases (Data from Birdetal &Rossini et al).

DETAILED DESCRIPTION

The present invention, then, is directed to a system which enables thedetermination of gas properties including specific heat, c_(p), andthermal conductivity, k at reference conditions. The system utilizes athermal pulse approach which is based on generating an energy ortemperature pulse in a heater, which is coupled to a sensor primarily bythe fluid medium (gas or liquid) of interest. Both quantities can bedetermined from a single pulse. The inventive method is based on thediscovery that thermal conductivity, k, and specific heat, c_(p), atreference conditions can be computed by sensing them only at othernon-reference conditions, without requiring compositional analysis.

The hypotheses which guided the search for this method were as follows:for limited ranges of gas composition, temperature and pressure thesensed property values may be related within acceptably small errors tothe reference conditions; and the chances of success are favored bythese facts: 1) thermal conductivity, molar or weight-based specificheat and viscosity, n, are largely pressure independent, especiallyaround low or environmental pressures, 2) temperature and temperaturedependences of k and c_(p) can be easily sensed by changing themicrobridge heater temperature, should this be needed to enhance themethod's accuracy, 3) thermal conductivity and specific heat aresomewhat related, see FIG. 18, although such relation is disturbed bythe presence of non-hydrocarbons like N₂, CO₂, CO, H₂, etc., all ofwhich are generally present but only in low concentrations in normalfuel gases, except city gas and peak shaving gas, 4) such gas propertyrelations have been used to determine absolute gas pressure, and 5) thetemperature dependencies of k and c_(p) do not vary much from gas togas, see FIGS. 19, 20 and 21.

The chances of success are hindered by the fact that 1) themicrobridge-sensed specific heat is volume-based and therefore dependenton absolute pressure and, as mentioned above, 2) non-hydrocarbon gasconcentrations complicate the relation between k and c_(p) of naturalgases.

Table 1 shows the result of deriving a number of algorithms to computek_(s) and c_(ps), i.e., the properties at standard or referenceconditions of temperature, T_(s) (and P_(s)), which were chosen as 60°F.(15.555° C.) and 14.73 psia (1 atm). The actual computations were madefor 15° C. higher to allow for the influence of the microbridge heateron raising the average gas temperature around it. The set of over 60natural gases used to derive these algorithms were chosen asrepresentative for their territory, and contain less than 2% each of N₂or CO₂, no more than 0.1% O₂, and no less than 85% CH4. The chosentemperature range is from -12.2° to 45.6° C. (10° to 114° F.).

As shown, the standard errors of the algorithm vary from 5000 ppm (0.5%)down to 153 ppm, with maximum errors about 3 to 4×larger. For claritysake the exponents of the listed polynomials have been omitted, althoughall are of the general form:

    where 1/k.sub.s or 1/c.sub.ps or k.sub.s or c.sub.ps may be represented as Y, where Y=A+BT.sup.b +Ck.sup.c +Dc.sub.p.sup.d +E(kT.sup.x).sup.e +F(c.sub.p T.sup.V).sup.f +G(dk/dT).sup.g +H(dc.sub.p /dT).sup.h.(This is equation 1)

with one or more of the terms missing in order to simplify theexpressions as much as possible.

The algorithms listed in Table 1 (an abreviated Table) are preferredbecause the two marked by asterisks achieved the lowest error, whilethose marked with an "L" are preferred because they achieved areasonably low error without requiring measurements at more than onemicrobridge heater temperature (low cost compromise).

The choices which were considered in converting the measured k and c_(p)from the measurement* to the reference temperature (60° F., 15.555° C.)values k_(s) and c_(ps) are expressed in terms of the followingfunctional relationships:

                  TABLE 1                                                         ______________________________________                                        CONVERSION OF K AND C.sub.P TO REFERENCE                                      TEMPERATURE                                                                                        Errors                                                                        Std.  Max.   Log.                                                             PPM   PPM    Sens.                                       ______________________________________                                        (L) k.sub.s                                                                          = A + BT + Ck + D (kT)                                                                            287     1931 2.00                                  (*) k.sub.s                                                                          = A + BT + Ck + D (dk/dT)                                                                         153                                                (*) 1/c.sub.ps                                                                       = A + BT + Cc.sub.p + Ddc.sub.p /dT                                                               165                                                (L) c.sub.ps                                                                         = A + BT + C (c.sub.p /T).sup.c +                                                                 197      660 1.51                                         D (kT)                                                                 ______________________________________                                    

Where A, B, C, D are the coefficients determined by least squaresregression method and are listed in Table 2.

The coefficients and exponents for these four preferred algorithms areas follows, with all k-values in microcal/(s^(o) Ccm), c_(p) incal/(mol°C), T in °K:

                  TABLE 2                                                         ______________________________________                                        Ref. Prop. and Eq. #:                                                         k.sub.s, 2  k.sub.s, 3                                                                              c.sub.ps, 4                                                                              c.sub.ps, 5                                  ______________________________________                                        A:  51.39659    61.2175   52.75219 4.522849                                   B:  -.005233625 -.0163255 -26.85281                                                                              -278217.8                                  b:  1.623819    1.4605    .07655509                                                                              -2.01471                                   C:  1.401951    1.5920    -1361.898                                                                              556.745                                    c:  .96102173   .91548    -2.900177                                                                              1.235544                                   D:  -.9721519 ·                                                                      -182934   4.02644 · 10.sup.7                                                            3.199885 · 10.sup.15                  10.sup.-5                                                                 d:  1.140100    12.317    4.407289 -3.834833                                  and equation #6:                                                               ##STR1##                                                                     where x = (T/T.sub.o)                                                         ______________________________________                                    

Eq. (6) above was also discovered during this study and is listed hereas an additional, very useful relation.

As shown, the top two algorithms only involve inputs of thermalconductivity properties, while the bottom one requires both k and c_(p)inputs to compute c_(ps).

Measurement of c_(p) with microbridge sensors have to date yielded theresult in units of energy/(volume×degree), which are pressure dependent.While this does not concern the first two preferred algorithms describedabove for k, it does affect those for c_(ps), using sensed values ofc_(p). This limitation is overcome by determining the pressure (withoutadditional sensors!), computing the molar volume V_(M) =V_(Mo) (T/T_(o))(1/P); where V_(Mo) is 22415(T_(o) /273.15) cm³ /mol, T in °K and P inatm; and then obtaining c_(p) =c_(pv) V_(M) in units of cal/(mol °K).

Thus the ability to convert one set of fluid or gas properties sensed atone condition of T and P to another or reference condition of T_(o) andP_(o), without knowing its composition or pressure, was proven to beachievable with errors as small as 153 ppm, for limited ranges ofcomposition and temperature. Several options were developed which varyin accuracy and computational (and sensing system) complexity. Even ifc_(p) is sensed on a volumetric basis (c_(pv) in cal/(cm³ C)), whichmakes it pressure and temperature dependent, the method is applicable byfirst computing pressure from sensed k and c_(pv) (volumetric).

The System

In order to more fully appreciate the microbridge flow sensor systemupon which the present method invention is utilized to extend theapplicability thereof, the following description is supplied.

Thermal conductivity and specific heat of each fluid of interest producecharacteristic transient and steady-state temperature reactions in aproximate sensor as exemplified in FIG. 6.

In the preferred implementation, specific temperatures, as T₁ and T₂ inFIG. 6, are selected as "marker" points with respect to the sensor.These marker points are used to reference the determination of the timeperiods, as t₁ -t₂, required to achieve the corresponding temperaturerise(s) or fall(s) in the sensor(s) between the marker points. As willbe discussed, the sensor or sensors are located in predetermined spacedrelation to the heater or heaters, but preferably physically separatedtherefrom so that the proximate influence of the solid heatermaterial(s) is reduced and the coupling of the heater with the sensor orsensors by the fluid of interest is relatively enhanced.

The preferred embodiments of the approach of the invention contemplatedisposing spaced microspec sized heating and sensing elements in arelatively static (zero flow) sample of the fluid of interest. Themicrosensor system or "microbridge" system, as it will be referred toherein, though not limiting, is presently preferred for several reasons.The system is extremely fast reacting, is very accurate, very sensitivebecause of its advantageous coupling to the fluid of interest and smalland adaptable to a variety of configurations.

The microbridge semiconductor chip sensor contemplated, for example, incertain embodiments preferred for the invention may resemble the form ofone or more of the microbridge systems illustrated in the patentsidentified above. Such a system is exemplified by FIGS. 1-5 taken fromU.S. Pat. No. 4,501,144. A discussion of that example will now bepresented as it will be helpful in understanding the present invention.While the present discussion is believed sufficient, to the extentnecessary, any additional material contained in the microbridge relatedpatents cited is deemed to be incorporated herein by reference.

The illustrated embodiment of FIGS. 1-5 contemplates a pair of thin filmtemperature sensors 22 and 24, a thin film heater 26 and a base 20supporting the sensors and heater out of contact with the base. Sensors22 and 24 are disposed on opposite sides of heater 26. Body 20 is asemiconductor, preferably silicon, chosen because of its adaptability toprecision etching techniques and ease of electronic chip producibility.The embodiment includes two identical temperature sensing resistor grids22 and 24 acting as the thin film heat sensors and a centrally locatedheater resistor grid 26 acting as the thin film heater.

Sensors 22 and 24 and heater 26 may be fabricated of any suitable,stable metal or alloy film. In FIG. 8, the metal used was a nickel-ironalloy sometimes referred to as permalloy, with a composition of 80percent nickel and 20 percent iron. The sensor and heater grids areencapsulated in a thin film of dielectric, typically comprising layers28 and 29 and preferably silicon nitride, Si₃ N₄, to form thin filmmembers. In the embodiment shown in FIGS. 1 and 2, the sensor comprisestwo thin film members 32 and 34, member 32 comprising sensor 22 and 34comprising sensor 24, each member comprising one-half of heater 26 andhaving a preferred dimension of 150 microns wide and 400 microns long.

The embodiment of the system further describes an accurately defined airspace 30 which contemplates air space effectively surrounding elements22, 24, 26. The effectively surrounding air space is achieved byfabricating the structure on silicon surface 36, thin film elements 22,24 and 26 having a preferred thickness of approximately 0.08 to 0.12micron with lines on the order of 5 microns wide and spaces betweenlines on the order of 5 microns, the elements encapsulated in a thinsilicon nitride film preferably having a total thickness ofapproximately 0.8 microns or less, and by subsequently etching anaccurately defined air space, of about 100 microns deep, into siliconbody 20 beneath members 32 and 34.

Members 32 and 34 connect to top surface 36 of semiconductor body 20 atone or more edges of depression or air space 30. As illustrated in FIG.3, members 32 and 34 may be bridged across depression 30; alternately,for example, members 32 and 34 could be cantilevered over depression 30.

Heat flows from the heater to the sensor by means of both solid andfluid couplings there between. Of note is the fact that silicon nitride(Si₃ N₄) is a highly effective solid thermal insulator. Because theconnecting silicon nitride film within members 32 and 34 is a goodinsulator, heat transmission through the solid does not dominate thepropagation of heat from heater 26. This further enhances the relativeamount of the heat conducted to sensing resistor 22 and 24 from heaterresistor 26 by flow through the surrounding fluid rather than throughthe supporting nitride film. Moreover, the supporting silicon nitridefilm has a low enough thermal conductivity that sensing resistor grids22 and 24 can be located immediately adjacent or juxtaposed to heatingresistor grid 26. Thus, sensing resistor grids 22 and 24 are in effectsuspended rigidly in the air space proximate heater resistor 26 and actas thermal probes to measure the temperature of the air near and in theplane of heater resistor grid 26.

The operation of the system in sensing air flow is described in detailin the above-referenced U.S. Pat. No. 4,501,144. Typical circuitimplementation is discussed briefly with reference to FIGS. 4 and 5 toadd some insight. The heater control circuit illustrated in FIG. 4 usesa Wheatstone bridge 46 which further typically includes heater resistor26 and a resistor 40 in its first leg and a resistor 42, heat sinkresistor 38, and a resistor 44 in its second leg. An error integratorincludes amplifiers 48 and 50 keeps bridge 46 balanced by varying thepotential across it and thus the power dissipated in heater resistors26.

The circuitry of FIG. 5 monitors the resistance difference betweendownstream sensor 24 and upstream sensor 22. This circuitry includes aconstant current source 52 comprising an amplifier 72 and a differentialamplifier 54 further including amplifiers 68 and 70. The constantcurrent source drives a Wheatstone bridge comprising two high impedanceresistors 56 and 58 in one leg and the two sensing resistors 22 and 24with a nulling potentiometer 60 in the other leg. The gain ofdifferential amplifier 54 is adjusted by potentiometer 62. Output 64provides an output voltage that is proportional to the resistancedifference between the two sensing resistors 22 and 24.

To get some concept of the small size of the microbridge, the powerrequired by heater resistor to heat such a device 200° C., for example,above ambient temperature is less than 0.010 watt. The exceedingly smallthermal mass of the heater and sensor element structures, theirexcellent coupling to the surrounding fluid because of a highsurface/volume ratio, and the thermal insulation provided by the thinsilicon nitride connecting them to the supporting silicon body, and thesurrounding air space, all contribute to produce a system well suited tofast and accurate sensing. Response time constants as short as 0.005second have been measured. Consequently, sensor elements can respondvery rapidly to proximate environmental changes.

Now with reference to the implementation of the present invention, FIGS.7a, 7b, and 7c, depict three slightly differing embodiments orconfigurations representative in terms of number and arrangement of theheaters and sensors which can be used in this invention. In FIG. 7a, incontrast to FIG. 1, all of the elements 122, 124 and 126 are used asheaters. FIG. 7b is an embodiment which is similar to the embodiment ofFIG. 1 with thin film element 126 acting as heater and elements 122 and124 acting as sensors. The embodiment of FIG. 7c, represents thepreferred arrangement in which the element 122 acts as heater andelement 124 acts as sensor. The effective gap and thus the thermalisolation between heater and sensor is desirably wider in the embodimentof FIG. 7c.

The actual general geometric structure of the embodiments of FIGS. 1-3,and 7a-7c is more clearly illustrated in the scanning electronmicrograph (SEM) photo of FIG. 8. The precision with which the cavityand bridge elements ar defined and located in spaced relation, as FIG. 8depicts, is particularly noteworthy. The SEM represents a magnificationsuch that the indicated length of 0.010" appears as shown.

In the implementation of the invention disclosed herein particularattention is directed to (1) setting specific temperature markers in thesensor to determine the time periods needed for achieving thecorresponding temperature changes, (2) using temperature sensors whichare physically separated from the heater so that the direct influence ofthe heater and heat conducted to the sensor other than via the fluid ofinterest is reduced, and (3) using a pulse which reaches at least amomentary steady-state plateau to determine k, which then is used withthe transient measure to determine c_(p).

FIG. 6 graphically depicts a square wave electrical energy pulse 130 tothe heater as at 126 which results in quasi square wave heat pulsesreleased by the heater. These in turn, result in reactive curves as at131, 132 and 133 at the sensor which vary as described below. The pulseapplied to the heater, for example, may have a height of about 4 voltswith a pulse width of 100 ms. Since the heater is closely coupledthrough the fluid medium to the sensors, the family of curves 131, 132and 133 resembles the shape of the input pulse 130. They show the heatresponse in the sensors 122 and 124. FIG. 11 represents an oscilloscopetrace showing temperature rise and fall versus time for dry air atatmospheric pressure. It uses a different scale for time than does FIG.6, but illustrates the curve form produced by the pulsed input. Thecurves generally include beginning and ending transient portionsflanking a relatively steady-state central portion. The relatively quickresponse of the sensor allows a relatively long steady-state to existeven with a pulse of 100 ms. Of course, the curves are affected byfactors such as pressure and temperature as they influence the effectivethermal conductivity and specific heat of the particular fluid ofinterest.

Heat flowing from the heater element or elements to the sensor elementor elements is conducted both through the fluid and through the solidsemiconductor element support substrate or the like. It is advantageouswith respect to the measurement of k or c_(p) of the fluid of interestthat the amount of heat reaching the sensor through the solidconnections be minimized so that substantially all the measured thermaleffect is generated via the fluid of interest.

With respect to the transfer of heat to the sensor(s) some backgroundinformation regarding the propagation of heat or temperature waves ispresented. The speed of propagation, v, of a one dimensional wave (if itfeatures an exponential decay profile) is constant and given by theexpression:

    V=D.sub.T /a=(D.sub.T /b).sup.0.5,                         (1)

where:

a is an exponential decay constant

b is the rise time constant at a fixed location and

D_(T) is the thermal diffusivity.

A complete list of nomenclature and subscripts with units appears inTable I, below. D_(T) is related to k and c_(p) by the expression

    D.sub.T =k/c.sub.p                                         (2)

D_(T), therefore, if known, may be a key to obtaining c_(p). The risetime constant, b, was measured to be about 4 msec. For typical gases,D_(T) ranges from 1.7 cm² /s for He to 0.054 cm² /s for C₃ H₈. Metalsexhibit high values such as 1.7, 1.1 and 0.18 cm² /s respectively forAg, Cu and Fe. Insulators, however, are even lower than the gases at0.004 cm² /s for glass and 0.0068 cm² for Si₃ N₄ which, as discussedabove, is a good insulator. The propagation speed, v, in a typical gassample then is about (1/0.004)⁰.5 =15 cm/s. This compares with(0.0068/0.004)⁰.5 =1.3 cm/s for Si₃ N₄, assuming that the same rise timeconstant of about 4 ms is applicable to both the one measured in the Si₃N₄ and the actual one in the gas.

The effect is that the influence of the temperature wave propagatingfrom one thin film strip, that is, the heater, to a second thin filmstrip, the sensor, both being embedded in a membrane of Si₃ N₄, isfaster for the gas than for the Si₃ N₄. This also supports the choice ofa material such as Si₃ N₄, since it reduces the contribution of heatflow through the solid media. This is beneficial to the accuracy of thesystem.

Typical microbridge embodiments are illustrated by FIGS. 7a-7c. Theywill now be explained in greater detail.

    ______________________________________                                        NOMENCLATURE TABLE (I)                                                        Symbol                    Units                                               ______________________________________                                                  Exponential Decay Constant                                                                        cm                                              a.sub.1 -a.sub.n                                                                        Constant                                                            A         Area of Heat Transfer to                                                                          cm.sup.2                                                  Microbridge or to Gas                                               b         Rise Time Constant at a                                                                           °C./s                                              Fixed Location                                                      cp        Specific Heat       cal/(cm3 °C.)                            D.sub.T   Thermal Diffusivity,                                                                              cm.sup.2 /s                                               D.sub.T = k/c.sub.p                                                 k         Thermal Conductivity                                                                              cal/(sm °C.)                             L         Length of Thermal Conductance                                                                     cm                                                        Path in Gas or Solid                                                P         Pressure of Gas     psia                                            Q         Power of Heat Release Rate                                                                        watts                                           R.sub.o   Resistance at Room Temperature                                                                    ohms                                            t         Time                s                                               T         Absolute Temperature                                                                              °C.                                      U         Bridge Output or Amplified                                                                        V                                                         Bridge Output                                                       V         Volume of Gas or Solid                                                                            cm.sup.3                                                  (Microbridge)                                                       v         Speed of Propagation                                                                              cm/s                                            x         Temperature coefficient                                                                           °C..sup.-1                                         of resistance                                                       SUBSCRIPTS                                                                    c         Conduction                                                          S         Microbridge or Solid                                                g         Gas                                                                 o         Room, Reference or Gas Tem-                                                   perature Without Microbridge                                                  Heating                                                             h         Heater or Hot                                                       m         Middle or Medium                                                    ______________________________________                                    

The configuration of FIG. 7a involves using the same microresistance122, 124, 126 for the heating pulse and the sensing task. In thisembodiment of the resistive heater-sensor element may be one leg of aconventional resistive Wheatstone bridge in a control circuit.

FIG. 7b depicts an arrangement wherein the center microresistancestructure 126 is used as a heater flanked by two symmetrically locatedouter sensing resistance elements 122 and 124. The elements 122 and 124are separated from the heater 126 by a narrow gap.

FIG. 7(c) shows an embodiment configuration in which the left element ofthe bridge 122 is used as the heating element and the right element 124as the sensor. This embodiment takes advantage of a rather large centralgap to achieve improved thermal isolation between the heater and thesensor.

FIG. 9 shows a modified control circuit which uses the centermicroresistance 126 as heater, while the sensing task is performed bythe two resistors 122 and 124. The dual heater sensor configurationcorresponds to FIG. 7b and the circuit is representative of typicalsensor/measurement circuit. FIG. 9 includes a timer 140 providingsquare-wave electrical pulses to the heater 126. The heater couples theheat pulse to the sensors 122 and 124 in the bridge 142. The output ofthe bridge is connected through an amplifier 143 to a pair ofcomparators 144 and 145 which operate "start" and "stop" inputs to acounter 146 which counts 10 mHz clock pulses. The counter counts measurethe time interval (t₂ -t₁) between temperatures T₂ & T₁ illustrated inFIG. 6.

FIG. 9a is similar to FIG. 9, but more detailed. The bridgeconfiguration is the heater-space-sensor configuration of FIG. 7c. Thesensor resistance arm of the microbridge is set into a Wheatstone bridge150 at 124. Another proximate resistive arm 122 is fed a voltage pulsefrom pulse generator 151 to provide a heat pulse into the microbridgeelement 126. The Wheatstone bridge 150 also may contain a nullingbalancing resistor 152 which can be used in the manner of potentiometer60 in FIG. 5 to initially zero the device. The microbridge resistorsensor 124 in the Wheatstone bridge receives the heat pulse from heaterelement 122 principally by thermal conduction through the surroundingfluid. Some conduction, of course, does occur through the solidmicrobridge substrate and surroundings.

The circuitry of FIG. 9a is conventional and can readily be explainedwith reference to its functional operation with regard to processing thebridge output signal. The voltage output signals of the bridge 150 areamplified by differential amplifiers 153 and 154 in a differentialamplifier section. The imbalance signal is further amplified by a highgain amplifier at 155. The signal at 156 as is the case with the signalat 147 in FIG. 9 is in the form of a DC voltage signal, U, the amplitudeof which is solely related to the thermal conductivity of the fluid ofinterest as will be discussed above.

The remainder of the circuitry of FIG. 9a includes a DC level clampingamplifier 157 and isolation amplifier 158. The temperature level,time-related switching and counting circuitry includes comparators 159and 160 together with Nand gates 161 and 162 having outputs which areconnected to the counter timing device (not shown) as in FIG. 9. Bymeasuring the time needed for the sensor temperature to rise or fallbetween two or more known temperature values or markers as representedby sensor resistance or bridge voltage outputs a measure related to thespecific heat per unit volume, c_(p) of the fluid of interest isobtained. The timing device may be a conventional 10 MHz pulse counteror the like. Again, this is illustrated schematically in FIG. 6.

The output signal from the Wheatstone bridge, U, represents the voltageimbalance caused by the temperature change in microbridge sensor orsensors induced by the corresponding heater pulse output. Because themagnitude of this imbalance is related directly to the amount of energyabsorbed by the sensor or sensors, the amplitude of the signal isdirectly related to the thermal conductivity, k, of the conducting mediain a manner next explained.

FIG. 6 shows that during much of the about 100 ms wide pulse period thetemperature of the sensor reaches and maintains a constant value. Duringthis time, the influence of the energy sink or source terms representedby specific heat are zero, which means that only thermal conductivitygoverns the value of the sensor temperature.

FIG. 12 is a plot of temperature rise in the form of bridge output, U,(FIG. 9 or 9a) using the sensing arrangement of FIG. 7(b) versus time inmilliseconds for various gases at atmospheric pressure. Curves formethane, dry air, ethane and a vacuum are presented. In this specificembodiment there was a heater resistance of 800 ohms, a pulse height of2.5 volts, and a pulse width of 100 ms. Temperature markers t, and t₂are shown on the graph. These markers relate to those of FIG. 13 whichshows a graphical presentation of heat up time versus pressure forseveral gases with a sensor-heater such as that shown in FIG. 7b andusing the T₂ -T₁, marked in FIG. 11.

The literature value of the thermal conductivity of several gases hasbeen plotted vs. the measured sensor temperature expressed directly interms of the measured Wheatstone bridge imbalance potential, U. Thisrelationship has been derived empirically for a microbridge of the typedepicted in FIG. 7(c) and is plotted in FIG. 13, using the least squaresmethod in a multiple regression analysis to achieve the best fit curve.The relation can be linearized over a modest span sufficient for thepurpose of the invention. Other combination configurations ofheater/sensor embodiments can likewise be calibrated using known gasesor gases of known k. Thus, using an off-the-shelf flow sensor of thetype 7(c) in the circuit 9(a), a 4.0 V pulse of 100 ms duration wasused.

This yielded an approximate linear relationship between U and k_(g) ofthe form

    k.sub.g =a.sub.4 U+a.sub.5                                 (3)

where

a₄ =-25.8807 and a₅ =181.778 for the above conditions.

The above then achieves the calibration of the sensor for k_(g). Thelinear approximation holds over enough of a span to provide accuratemeasurements. Similar relations may be derived under other measurementconditions including additional pressure correction terms.

Further details related to determining the coefficients for thealgorithms to compute c_(p) are described next. This determinationrequires that the measuring system be calibrated first, which consistsof determining the coefficients a₁, a₂, and a₃, of the algorithm to thencomputer c_(p).

Assuming a two-dimensional model for heat transfer in the microbridge,see FIGS. 7a-7c, the measured sensor temperature response may bedescribed with reference to the following processes (at zero gas flow):

1) Heat release by the heater element film.

2) Temperature build up in the heater element material (FeNi or Pt) andsurrounding support material (insulator Si₃ N₄), i.e. within the bridgematerial.

3) Conduction towards the sensor via a) the bridge material, and b) thefluid phase surrounding the bridge.

4) Temperature build up in the sensor material (as in heater material initem 2 above), and in the gas surrounding it by the heat arriving viathe above processes.

5) Achieving a steady-state distribution of temperature.

6) The revenue process to steps 1-5 during the start of the heateroff-period.

Further assuming, for the sake of simplicity, that the specific heats ofthe involved gaseous and solid materials do not depend on temperature,we can approximately describe the above processes by the followingexpressions (see Table I above for symbol explanation) using the sameprocess numbering as above:

1) Q=V² /(R_(o) (1+(T_(h) -T_(o))) for small temperature rises.

2) The heater temperature results from balancing the heat input andoutput rates: T_(h) -T_(o) =Q/(k_(s) A_(s) /L_(s) +k_(g) A_(g) /L_(g))with Q in watts; the temperature T_(h) is established in a time that isshort compared to the time it takes to reach the sensor if the sensor isnot identical to the heater, as in configurations 7(b) and 7(c).

3) In a truly one-dimensional case most of 50% of the released power Qeventually arrives at the sensor, since it only has two ways to go (+xand -x directions). In a two- (or even three-) dimensional case a majorpart of Q gets dissipated in the y and z directions, so that only afraction, Q_(c), is conducted to the sensor, with a corresponding dropof the original temperature, T_(h), down to an intermediate temperatureT_(m). The sensor then experiences an energy rate arrival of

    Q.sub.c =(T.sub.m -T.sub.o) (k.sub.s A.sub.s /L.sub.s +k.sub.g A.sub.g /L.sub.g)                                                 (4)

4) The sensor temperature rise rate is governed by the specific heat ofthe gas surrounding the sensor and the closely coupled material of thesensor itself so that:

    Q.sub.c =(dT/dt) c.sub.ps V.sub.s +(dT/dt)c.sub.pg V.sub.g (5)

The quantity measured and plotted in FIGS. 14, 15 and 16, is the time(dt) needed to raise the sensor temperature by an increment (dT) whichis chosen by the two or more sensor resistance value markerscorresponding to T₁ and T₂.

It is readily apparent from equation (5) that c_(pg) could be determinedfor an unknown gas if the various quantities entering in Eqs. (4) and(5) were either known or measurable. It has been found, however, thateven if only dt, dT, T_(o), P and k_(g) are conveniently measurable, theother quantities may be determined by calibration. This can be doneaccording to an invention as follows:

For calibration, gases of known composition (preferably but notnecessarily pure) and therefore of known specific heat and thermalconductivity at the used pressure and temperature (both also measured),are brought in contact with the sensor. The effect of the pulsed heatreleases is recorded in terms of the lapsed time, t₂ -t₁, as has beendescribed. After noting results for various gases, pressures, heatertemperatures and/or heating/cooling periods, with pulses of constanttemperature, voltage, current or power, the recorded time and conditiondata are entered into an array of data ports which can be used forautomatic or computerized data processing or other number crunchingtechniques.

The process can be illustrated with the help of equations (4) and (5),by way of example, without excluding other, similar approaches likely tooccur to one skilled in numerical analysis. With this in mind, thefollowing ports receive data or input for various gases, pressures (andtemperatures):

    ______________________________________                                        Ports:     Y          X1           X2                                         Inputs:    c.sub.pg P/P.sub.o                                                                       (t.sub.2 - t.sub.1) k.sub.g                                                                t.sub.2 - t.sub.1                          ______________________________________                                    

Known and available multiple linear regression analysis (MLRA, see FIG.10) program can determine the linear coefficients a₁, a₂, and a₃ (e.g.,by matrix inversion), which, together with the above input data, formsthe calibrated expression derived from equations (4) and (5) to computespecific heat, c_(p) :

    c.sub.pg P/P.sub.o =a.sub.1 (t.sub.2 -t.sub.1)k.sub.g +a.sub.2 (t.sub.2 -t.sub.1)-a.sub.3                                         (6)

The determined (calibration)coefficients, of course, represent thelumped factors of several sensor properties or conditions from equations(6) and (7): ##EQU1##

In order to minimize differences in T_(m) at the sensor location, themost advantageous operation from among constant temperature, voltage,current or power is chosen. The above method is demonstrated on thebasis of 1) constant voltage pulses, which result in quasi square waveheat pulses released by the heater, and 2) changes in gas type (CH₄, C₂H₆, air and O₂) and pressure; the chosen configuration was 7(b).

FIG. 14 shows the result of storing and plotting the dt=t₂ -t₁ andpressure data for each of the gases used, for which the c_(p) and kvalues can be obtained from the open literature. This relation islinearized by applying the least squares method in a multiple linearregression analysis to achieve the best fit line. After entering thesedata into the above ports Y, X1 and X2, the regression analysis programperformed. The obtained result was, for a configuration as in FIG. 7(b):

    a.sub.1 =-16509, a.sub.2 =3.5184 and a.sub.3 =0.005392     (7a)

Proof that the above calibration coefficients are valid is provided byFIG. 15, for example, in which these coefficients have been used togenerate the shown lines for CH₄, C₂ H₆, air and O₂. As shown, the linesindeed connect and agree with all experimental points. Additional lineshave been plotted with the c_(p) and k data of the literature for othergases as well.

The final step in using this calibration method involves known means tostore, write or burn in the obtained, tailored values of a₁, a₂ and a₃for the individual microbridge, which may be a Honeywell MICRO-SWITCHModel No. AWM-2100V, into the memory linked to it. The microsensor isthen ready for use to measure the specific heat of unknown gases,provided that P and k be known at the time of measurement.

FIG. 10 depicts a schematic block diagram of a device for measuringc_(p) and k. The system includes the signal processing circuitryindicated by 170, a multiple linear regression analysis (MLRA) unit 171for deriving the known equation constants for the particular microbridgeconfiguration and circuitry used, i.e., a₁ -a_(n), a data bank 172 forstoring calibration c_(p) and k data and an output interface unit 173.

With respect to the embodiment of FIG. 10, prior to use, fieldrecalibration may be accomplished simply by entering the P, c_(p) and kvalues of the test gas into the data bank. If P cannot be measuredindependently of the sensor already in the subject system its errors canbe incorporated as a correction in the c_(p) and k recalibration. Themeasured values of U and dt are then used as in the measurement mode todetermine sensor values of k and c_(p). If they disagree from theentered values the constants a₃ and a₅ may be modified to fit theentered or book values.

This approach may be a practical one for field use, but it should bechecked by using a second test gas. If that agrees, the recalibrationmay be completed. If not, a complete calibration of all a₁ -a₅coefficients should be made.

It should be mentioned that in all of the above discussion the influenceof temperature was not mentioned for the sake of simplicity. It is wellknown, however, that temperature does influence both c_(p) and k but canbe addressed, if necessary, in one of the following ways:

1) Controlled, (expensive and energy consuming) or

2) Compensated by special temperature-sensitive elements in the analogpart of the circuit, or

3) Entered into the sensor algorithm as an additional parameter, whichis sensed, e.g., by monitoring one of the many available temperaturedependent resistors on the sensor. This is the preferred approach forsensing systems requiring maximum accuracy.

With respect to use of the instrument of FIG. 10, the U and dt=t₂ -t₁(and P) signals obtained for an unknown gas are processed as follows inthis mode;

1) Computation of k from expression (3) using the coefficients a₄ and a₅which have been stored in (or burned into) the sensor's memory aftercalibration, and

2) Computation of c_(p) from expression (6). It should also be notedthat a pressure signal is also needed as a basic ingredient since c_(p)is used here in relation to a volume of gas as opposed to k which islargely pressure independent if the sensor is used at or aboveatmospheric pressure, at which the gas mean free path is small comparedto the characteristic dimensions of the involved sensor.

The graphical presentation of FIG. 16 depicts heating time inmilliseconds versus pressure and gas type and specifically showingcurves for methane, ethane, air and oxygen. The sensing configuration ofFIG. 7(c) was used. In this example, the pulse height was 1.75 voltswith a pulse width of 100 ms. and the heater and sensor resistance eachbeing about 2000 ohms. FIG. 17 depicts a cooling curve for the sameconfiguration as FIG. 16. Conditions were the same except that the pulseheight was 4.0 volts.

Of course, the output of the device can be in any desired form includinganalog or digital signals, printed records, etc., after the value isobtained.

I claim:
 1. A microsensor apparatus for determining fuel gas propertiesat reference conditions for a gas at unknown conditions comprising:asemiconductor microbridge structure supported by a substrate having anelectrically energizable heater film element thereon and resistivesensor film element(s) located proximate to the heater film elementhaving; a substrate temperature measuring means mounted on saidsubstrate wherein said substrate temperature measuring means is formeasuring gas-temperature-at-the-structure-substrate (T_(g)) from signalprovided by said substrate sensor; and such that said structure and saidsubstrate temperature measuring means are so arranged and disposed to bein contact by immersion in the gas to be sensed such that when anelectrical energy pulse is applied to said heater film element ofsufficient time duration and power, the pulse causes a resultingtransient temperature followed by a steady-state temperature in saidgas, to a degree detectable by said sensor(s) so as to produce animbalance output corresponding to the voltage imbalance due to change inresistivity between said sensor element (s) and balance resistorelements, integral s means for measuring the transient temperaturesignal based on said imbalance output called s and a means fordetermining the integral of said measurement over time, said signalbeing provided by said sensor(s), dU measuring means for measuring thesensor steady-state temperature signal called dU from signal based onsaid imbalance output, T_(e) measuring means for measuring ambient orelectronics temperature T_(e) from signal provided by said sensor(s),and a computing device connected to receive said signals dU, T_(g), andT_(e), and employing signal processing circuitry, data and processingcomponents, said computing device configured to have k computing means,c computing means and k_(s) computing means; havingk computing means forcomputing thermal conductivity of said fuel gas, k, as a function of dU,and T_(g) (gas temp) while compensating for ambient temperature, T_(e),influence on electronics receiving input from said dU, T_(g) and T_(e)means, c computing means for computing specific heat of said fuel gas,c_(p), as a function of dU, and T_(g) while compensating for ambienttemperature, T_(e), receiving input from said dU, T_(g) and T_(e) means,and k_(s) computing means for computing from computed k and measuredT_(g), k_(s) of said fuel gas (k at standard conditions) and an outputstructure for providing an output representative of at least one of k,c, or k_(s).
 2. The apparatus according to claim 1 in which thecomputing means for computing k and c follows the general form for1/k_(s) or 1/c_(ps) or k_(s) or C_(p) s of:

    A+BT.sup.b +Ck.sup.c +Dc.sub.p d+E(kT.sup.x).sup.e +F(c.sub.p T.sup.y).sup.f +G(dk/dT).sup.g +H(dc.sub.p /dT).sup.h     ( 1)

where k_(s) is thermal conductivity at standard or reference conditionsc_(ps) is specific heat at standard or reference conditions, and A, B,C, D, E, F, G, and H are coefficients, and b, c, d, e, f, g, h, x, and yare exponents.
 3. The apparatus according to claim 1 in which in themicrobridge structure has first and second resistive sensor filmelements located on opposite sides of and proximate to the heater filmelement.
 4. The apparatus according to claim 1 in which the electricalenergy pulse to the heater film approximates in form a square waveelectrical energy pulse.
 5. The apparatus according to claim 4 in whichthe pulse width of the electrical energy pulse is on the order of 100milliseconds.
 6. The apparatus according to claim 5 in which the pulseapplied to the heater film has a height on the order of 4 volts.
 7. Anapparatus as set forth in claim 1 and further comprising C_(ps) derivingmeans for computing specific heat at standard conditions, c_(ps), fromcomputed c_(p) and measured T_(g).
 8. The apparatus as set forth inclaim 5 and further comprising:W_(hc) means for measuring heater power,W_(hc), to achieve constant differential temperature, dT, above ambienttemperature wherein W_(hc) is also employed by k_(s) computing means inthe computing of thermal conductivity, k, as a function of dU, W_(hc)and T_(g) while compensating for the ambient temperature, T_(e),influence on the electronics and wherein W_(hc) is also employed by ccomputing means in the computing of specific heat at standard referenceconditions, called c_(ps), as a function of dU, W_(hc), and T_(g) whilecompensating for ambient temperature, T_(e).
 9. The apparatus accordingto claim 8 including a further step of employing said W_(hc) means formeasuring a different heater power, W_(hc2), to achieve another constantdT₂ above room temperature which leads to obtaining k₂ and c_(p2) inorder to be able to form dk/dT and dc_(p) /dT.
 10. The apparatusaccording to claim 9 in which the computing means for computing k or thecomputing means for computing c follows the general form for 1/k_(s) or1/c_(ps) or k_(s) or c_(ps) of:

    A+BT.sup.b +Ck.sup.c +Dc.sub.p.sup.d +E(kT.sup.x).sup.e +F(c.sub.p T.sup.y).sup.f +G(dk/dT).sup.g +H(dc.sub.p /dT).sup.h     ( 1)

where k_(s) is thermal conductivity at standard or reference conditions,c_(ps) is specific heat at standard or reference conditions, and A, B,C, D, E, F, G, and H are coefficients, and b, c, d, e, f, g, h, x, and yare exponents.
 11. A method to determine fuel gas properties atreference conditions for a gas at unknown conditions in microsensor fuelflow metering apparatus including the steps:providing a semiconductormicrobridge flow sensor having an electrically energized heater filmelement on a sensor substrate and first and second resistive sensor filmelements located on opposite sides of and proximate to the heater film;locating the flow sensor in immersed contact with the fuel gas;supplying an electrical energy pulse to said heater film of sufficienttime duration and power to cause a resulting transient temperaturesignal and a steady-state temperature signal in said sensors because ofthe resultant change in the temperature of the gas so as to produce animbalance output corresponding to resultant effects on the resistivityof said sensor film elements; measuring heater power, called W_(hc),required to achieve constant differential temperature, dT, above roomtemperature; measuring the rise in temperature due to the energy pulsebased on said imbalance output and determining its integral; measuringthe sensor steady-state output, dU; measuring gas temperature at thesensor substrate; and then, based on these measured signals:computingthermal conductivity of said fuel gas, k, as a function of dU, W_(hc),and the temperature of the gas at the substrate, T_(g), whilecompensating for ambient temperature; computing specific heat of saidfuel gas, c_(p), as a function of dU, W_(hc), and T_(g) whilecompensating for ambient temperature; from computed k and measured T_(g)computing a term called k_(s), which is k at standard conditions of saidfuel gas; from computed c_(p) and measured T_(g) computing a term calledc_(ps), which is specific heat of said fuel gas at standard conditions;and providing an output signal representative of at least one of saidcomputed values k, c_(p), k_(s) or c_(ps).
 12. The method according toclaim 11 including a further step of measuring a different heater power,W_(hc2), is measured, producing another constant, dT₂, above roomtemperature which can then be used by the k and c computing means toobtain k₂ and c_(p2) in order to then compute the values dk/dT anddc_(p) /dT.